I guess you meant you understod that most charge are constant current AT THE OUTPUT right?.
Right. There are two separate dimensions to this as I see it. One is what you measured, AC power consumption versus AC voltage at a given SOC. The other is AC power consumption at a given AC voltage versus DC output voltage which varies with the SOC. A charger that outputs constant current will draw an increasing amount of AC power as the battery charges. If a charger outputs a constant power, then then AC input power would also remain constant as the dc voltage varies with SOC. Of course power becomes low when constant voltage output is reached.
So either CC/CV or CP/CV charging could be done. Which one is better for the battery? CP would charge faster at low SOC than CC for the same maximum power. I don't know how the internal resistance of the battery varies with SOC but I'm sure it does. That would affect heating due to I^2R. There also might be other considerations with chemistry and such that would influence this choice. But disregarding the battery, it seems that constant power makes more sense. The AC input power required is then fixed and known, and the charging rate in kWh/h is constant rather than increasing with SOC. Right? Or does anyone really know?
BTW the legend for your chart shows five variables, but I only see three lines. Volts out is almost constant so unimportant and current out is not shown although it seems to have basically two constant values. So what I was asking is would the current out values stay constant or vary with SOC?